Answer:
The rest of the question is the attached figure.
Construct the line segment AC
As shown at the graph:
∠BAD = 110° and ∠C = 20°
∴∠BCD = 20° (Vertically opposite angles).
∠CDA = 180°-65° = 115°
∠B = 360 - (∠A+∠D+∠C) = 360 - (110 + 115 + 20) = 115°
Now in ΔACB and ΔACD
AC = AC (common)
AB = AD (given)
∠CBA =∠CDA (proved)
ΔACB ≅ ΔACD
∵ CPCTC ⇒ ∴ CB = CD
So, AD = AB and CB = CD (adjacent sides are equal)
∠D =∠B (A pair of opposite angles equal)
∴ ABCD is a kite .
